Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
ifstream fin("date2.in");
ofstream fout("date2.out");
int main() {
  int n;
  double h, afis[1002];
  cin >> n >> h;
  double arie = h / 2, aINIT;
  double crr_base = 1;
  double a, b, c, delta, sol;
  arie /= n;
  aINIT = arie;
  b = 2 * crr_base;
  a = -1.0 / h;
  for (int i = 1; i < n; ++i) {
    c = -2 * arie;
    delta = b * b - 4 * a * c;
    delta = sqrt(delta);
    sol = (-b + delta) / (2.0 * a);
    afis[i] = h - sol;
    arie += aINIT;
  }
  for (int i = n - 1; i >= 1; --i)
    cout << setprecision(10) << fixed << afis[i] << " ";
  return 0;
}